Friction Force Measurement in Reciprocating Tribometers A G Plint – STLE 2011 Abstract The transfer function of measuring systems for friction in tribological experiments is rarely analysed. This is of concern in reciprocating experiments, where claimed effects are not actual friction effects, but measurement artefacts or system resonance. For a measuring system with a fixed signal bandwidth, increasing the reciprocating frequency causes the apparent mean force to fall, giving the appearance of a reduction in friction with increasing frequency. As reciprocating frequency increases relative to the frequency response of the measuring system, the information content of the signal decreases. The transition from static to dynamic friction at the beginning of each stroke “plucks” the force measuring system. The magnitude of the resulting oscillations is a function of the magnitude of the plucking force and the rate of decay of the resulting vibration is a function of the resonant frequency of the measuring system and the variable damping coefficient of the frictional contact.
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Friction Force Measurement in Reciprocating
Tribometers A G Plint – STLE 2011
Abstract
The transfer function of measuring systems for friction in tribological
experiments is rarely analysed. This is of concern in reciprocating experiments,
where claimed effects are not actual friction effects, but measurement artefacts
or system resonance.
For a measuring system with a fixed signal bandwidth, increasing the
reciprocating frequency causes the apparent mean force to fall, giving the
appearance of a reduction in friction with increasing frequency. As reciprocating
frequency increases relative to the frequency response of the measuring
system, the information content of the signal decreases. The transition from
static to dynamic friction at the beginning of each stroke “plucks” the force
measuring system. The magnitude of the resulting oscillations is a function of
the magnitude of the plucking force and the rate of decay of the resulting
vibration is a function of the resonant frequency of the measuring system and
the variable damping coefficient of the frictional contact.
Introduction
Measurement of a dynamic force presents a number of challenges, frequently
ignored, when that dynamic force is associated with a tribological experiment.
Rarely, if ever, do published papers make any reference to the transfer function
of the measuring system used to sense friction. Although this is by no means a
new problem, this paper aims to explore key issues associated with nominal
friction force measurements in reciprocating tribometers, with particular
reference to well established commercially available test machines. The same
concerns apply to other dynamic friction devices, such as engines fitted with
floating pistons for ring/liner friction force measurement.
The motivation for writing the paper has been receipt of numerous requests to
comment on and explain dynamic friction force signals and how these should be
filtered and processed. It is clear that many “claimed” friction effects are not
actually real friction effects, but are either measurement artefacts or system
resonance. Two key issues will be explored in this paper, firstly, the effect of
frequency response of a measuring system and, secondly, the effect of the
transition from static friction to dynamic friction on measuring system
resonance, but our starting point will be a brief review of system response and
sampling rates.
Frequency Response of Measuring Systems
The information content available in the signal channels of a dynamic testing
machine is directly related to the signal bandwidth. The fundamental limitation
in most measuring systems is the bandwidth of the transducer itself.
It is generally accepted that, in order to keep measuring errors low, a
measuring system should not be used at frequencies above about 0.3 of its
resonant frequency and input filtering is imposed to limit the signal bandwidth
accordingly.
It is normal to apply filtering on measuring channels in order to eliminate higher
frequency signal noise and aliasing. The same characteristic filter should be
used on all channels, especially in high frequency systems, to ensure that the
information from different channels can be directly correlated and is not subject
to differing time delays, in other words, phase shifts between signals.
When sampling the signals processed by a filter it is important to sample at
high enough a rate to preserve the information in the original signal. The
Nyquist Sampling Theory indicates that the minimum acceptable sampling rate
is twice the maximum detectable frequency. The measured amplitudes of
signals at half the Nyquist sampling rate are attenuated to 64% of their true
value. The Sampling rate of the system should thus be well matched to its
signal bandwidth in order to preserve information content.
Aliasing
Aliasing occurs when the sampling rate is too low for the frequency response of
the system. As a simple example of aliasing, consider sampling the levels of
illumination by looking out of the window, at the same time, just once per day.
If the observations were always made at midnight, the collected data would
imply that it was always dark outside. If the observations were always made at
midday, the collected data would imply that it was always light outside.
Now, assuming that there are twelve hours of darkness and twelve hours of
light, consider taking three samples per day, at eight hours interval. If sampled
at 1200, 2000 and 0400, the observations will indicate twice as much dark as
light. If sampled at 0000, 0800 and 1600, the observations will indicate twice
as much light as dark.
As the signal is varying twice per day (from day to night) the absolute minimum
sampling rate in order to avoid aliasing would be four equi-spaced observations